Finite Group Databasebeta

← C2×#11747356 #14427949

Subgroups — C2×#11747356 #14427949

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91784C211yesmaximal, characteristic
2C2×#91390C211yesmaximal, characteristic, complemented
3C22×#6658C211yesmaximal, characteristic, complemented
4C22×#6651C211yesmaximal, characteristic, complemented
5C2×C5×#807C211yesmaximal, characteristic, complemented
6C2×C3×#3942C211yesmaximal, characteristic, complemented
7C2×#90969C211yesmaximal, characteristic, complemented
8#11747356C218yesmaximal, direct product factor
9C2×#65175—31nomaximal, Hall
10C22×D60—21no—
11C22×D60C2211yescharacteristic
12C22×C4×D15C2211yescharacteristic
13C22×C3×Dic10C2211yescharacteristic
14C2×C3×C5×C4⋊C4C2211yescharacteristic
15C2×#6714—21no—
16#91784—22no—
17#91784C2214yes—
18C2×C5×C4⋊Dic3C2211yescharacteristic
19C22×C5×C3⋊C8C2211yescharacteristic
20C22×C3×#168C2211yescharacteristic
21C2×Dic3⋊Dic5—21no—
22C2×#6667—21no—
23#91390—22no—
24#91390C2214yescomplemented
25C2×#6658—24no—
26C2×#6658C2214yescomplemented
27C2×#6651—24no—
28C2×#6651C2214yescomplemented
29C5×#807C2214yescomplemented
30C3×#3942C2214yescomplemented
31#90969C2214yescomplemented
32C2×#4812—51nomaximal, Hall
33C22×#677—31no—
34C22×#676—31no—
35C2×#4043—31no—
36C2×#4041—31no—
37C2×C5×#107—31no—
38C2×#3942D311yescharacteristic, complemented
39C2×#3941—31no—
40#65175—38no—
41C23×D15—21no—
42C23×D15D411yescharacteristic
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5C2311yescharacteristic
45C22×Dic15D411yescharacteristic
46C2×D60—22no—
47C2×D60—22no—
48C2×D60—24no—
49C2×D60—21no—
50C2×D60—44no—
51C2×D60C2312yes—
52C2×C4×D15—22no—
53C2×C4×D15—22no—
54C2×C4×D15D412yes—
55C2×C4×D15C2312yes—
56C22×C5×Dic3—21no—
57C22×C3×Dic5—21no—
58C2×C3×Dic10—22no—
59C2×C3×Dic10—22no—
60C2×C3×Dic10—21no—
61C2×C3×Dic10C2312yes—
62C3×C5×C4⋊C4—21no—
63C3×C5×C4⋊C4C2312yes—
64#6714—24no—
65C5×C4⋊Dic3—21no—
66C5×C4⋊Dic3C2312yes—
67C2×C5×C3⋊C8D414yescomplemented
68C2×C5×C3⋊C8C2312yes—
69C2×C3×#168—22no—
70C2×C3×#168C2312yes—
71Dic3⋊Dic5—24no—
72#6667—24no—
73#6658—28no—
74#6651—28no—
75C2×#946—51no—
76C22×#215—51no—
77C22×ΓL(1,𝔽25)—51no—
78C2×#895—51no—
79C2×C3×#103—51no—
80C2×#821—51no—
81C2×#807D511yescharacteristic, complemented
82#4812—58no—
83C22×D20—31no—
84C22×D20—61no—
85C22×C4×D5—31no—
86C22×Dic10C2×D311yescharacteristic
87C22×C5×C8—31no—
88C2×C5×C4⋊C4—31no—
89C2×C5×C4⋊C4C2×D311yescharacteristic
90C2×#685—61no—
91C2×#685—61no—
92C2×C4⋊Dic5—61no—
93C22×#168C2×D311yescharacteristic
94C2×#677—34no—
95C2×#677—64no—
96C2×#676—34no—
97C2×#676—64no—
98#4043—34no—
99#4043—62no—
100#4041—34no—
101#4041—62no—
102C5×#107—34no—
103#3942C2×D314yescomplemented
104#3941—34no—
105C2×#468—151noSylow
106C23×C3×C5C2×D411yescharacteristic
107C22×D15—22no—
108C22×D15—22no—
109C22×D15—22no—
110C22×D15—22no—
111C22×D15—42no—
112C22×D15—42no—
113C22×D15—42no—
114C22×D15C2×D412yes—
115C2×C3×C4×C5—22no—
116C2×C3×C4×C5—42no—
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5C2×D412yes—
119C2×C3×C4×C5#4112yes—
120C2×C3×C4×C5C2411yescharacteristic
121C2×Dic15—22no—
122C2×Dic15C2×D412yes—
123D60—22no—
124D60—22no—
125D60—48no—
126D60—42no—
127C4×D15—24no—
128C4×D15—22no—
129C4×D15—22no—
130C2×C5×Dic3—22no—
131C2×C5×Dic3—42no—
132C2×C3×Dic5—22no—
133C2×C3×Dic5—42no—
134C3×Dic10—22no—
135C3×Dic10—22no—
136C3×Dic10—42no—
137C3×#168—22no—
138C5×C3⋊C8C2×D414yescomplemented
139C22×C3×Q8—51no—
140C22×D12—51no—
141C22×D12—101no—
142C22×C4×D3—51no—
143C22×C3×C8—51no—
144C2×C3×C4⋊C4C2×D511yescharacteristic
145#946—54no—
146#946—102no—
147C2×#215—54no—
148C2×#215—104no—
149C2×(C2×D3)⋊C4—101no—
150C2×(C2×D3)⋊C4—101no—
151C2×C4⋊Dic3C2×D511yescharacteristic
152C2×Dic3⋊C4—101no—
153C22×C3⋊C8C2×D511yescharacteristic
154C2×ΓL(1,𝔽25)—54no—
155C2×ΓL(1,𝔽25)—104no—
156#895—54no—
157#895—102no—
158C3×#103—54no—
159#821—54no—
160#807C2×D514yescomplemented
161C23×D5—31no—
162C23×D5—61no—
163C22×C4×C5—21no—
164C22×C4×C5—61no—
165C22×C4×C5C22×D311yescharacteristic
166C22×Dic5—21no—
167C22×Dic5—31no—
168C2×D20—32no—
169C2×D20—62no—
170C2×D20—62no—
171C2×D20—64no—
172C2×D20—61no—
173C2×D20—124no—
174C2×C4×D5—32no—
175C2×C4×D5—32no—
176C2×C4×D5—62no—
177C2×C4×D5—62no—
178C2×Dic10—22no—
179C2×Dic10—22no—
180C2×Dic10—21no—
181C2×Dic10C22×D312yes—
182C2×C5×C8—34no—
183C2×C5×C8—32no—
184C5×C4⋊C4—21no—
185C5×C4⋊C4—32no—
186C5×C4⋊C4—61no—
187C5×C4⋊C4C22×D312yes—
188#685—64no—
189#685—64no—
190C4⋊Dic5—64no—
191C2×#168—22no—
192C2×#168C22×D312yes—
193#677—68no—
194#676—68no—
195C22×SD16—151no—
196C22×M16—151no—
197C2×C22⋊Q8—151no—
198C2×#121—151no—
199#468—158no—
200C2×#107—31no—
201C2×#103—51no—
202C2×#102—151no—
203C22×C3×C5#12112yes—
204C22×C3×C5AGL(1,ℤ/8)12yes—
205C22×C3×C5#13712yes—
206C22×C3×C5C22×D411yescharacteristic
207C2×D15—22no—
208C2×D15—22no—
209C2×D15—22no—
210C2×D15—44no—
211C2×D15—42no—
212C2×D15—42no—
213C2×D15—42no—
214C2×D15—84no—
215C3×C4×C5—42no—
216C3×C4×C5#12112yes—
217C3×C4×C5C22×D411yescharacteristic
218C3×C4×C5C2×#4111yescharacteristic
219Dic15—22no—
220C3×Dic5—42no—
221C5×Dic3—42no—
222C23×D3—51no—
223C23×D3—101no—
224C2×C3×Q8—52no—
225C2×C3×Q8—101no—
226C2×C3×Q8—102no—
227C2×C3×Q8—102no—
228C22×C3×C4—21no—
229C22×C3×C4—101no—
230C22×C3×C4C22×D511yescharacteristic
231C22×Dic3—21no—
232C22×Dic3—51no—
233C2×D12—52no—
234C2×D12—102no—
235C2×D12—102no—
236C2×D12—104no—
237C2×D12—101no—
238C2×D12—204no—
239C2×C4×D3—52no—
240C2×C4×D3—52no—
241C2×C4×D3—102no—
242C2×C4×D3—102no—
243C2×C3×C8—52no—
244C2×C3×C8—102no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4C22×D512yes—
247#215—108no—
248(C2×D3)⋊C4—104no—
249(C2×D3)⋊C4—104no—
250C4⋊Dic3—21no—
251C4⋊Dic3C22×D512yes—
252Dic3⋊C4—104no—
253C2×C3⋊C8D2014yescomplemented
254C2×C3⋊C8C22×D512yes—
255ΓL(1,𝔽25)—108no—
256C23×C5D3×D411yescharacteristic
257C22×D5—32no—
258C22×D5—62no—
259C22×D5—62no—
260C22×D5—62no—
261C22×D5—62no—
262C22×D5—122no—
263C22×D5—122no—
264C22×D5—122no—
265C2×C4×C5—22no—
266C2×C4×C5—42no—
267C2×C4×C5—62no—
268C2×C4×C5—122no—
269C2×C4×C5#23512yes—
270C2×C4×C5D3×D412yes—
271C2×C4×C5D3×D411yescharacteristic
272C2×C4×C5C23×D311yescharacteristic
273C2×Dic5—22no—
274C2×Dic5—32no—
275C2×Dic5—42no—
276C2×Dic5—62no—
277D20—62no—
278D20—62no—
279D20—128no—
280D20—122no—
281C4×D5—64no—
282C4×D5—62no—
283C4×D5—62no—
284Dic10—22no—
285Dic10—22no—
286Dic10—42no—
287C5×C8—34no—
288#168—22no—
289C22×Q8—51no—
290C22×D4—151no—
291C22×D4—301no—
292C23×C4—151no—
293C2×SD16—154no—
294C2×SD16—304no—
295C2×M16—154no—
296C2×M16—304no—
297C22×C8—31no—
298C22×C8—51no—
299C22⋊Q8—154no—
300C22⋊Q8—302no—
301#121—154no—
302#121—302no—
303C2×C4⋊C4—31no—
304C2×C4⋊C4—301no—
305C2×C4⋊C4D3×D511yescharacteristic
306C2×C22⋊C4—301no—
307C2×C22⋊C4—301no—
308#107—34no—
309#103—54no—
310#102—154no—
311C2×C3×C5#46814yescomplemented
312C2×C3×C5C2×#12111yescharacteristic
313C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
314C2×C3×C5C2×#13711yescharacteristic
315D15—42no—
316D15—82no—
317C23×C3D4×D511yescharacteristic
318C22×D3—52no—
319C22×D3—102no—
320C22×D3—102no—
321C22×D3—102no—
322C22×D3—102no—
323C22×D3—202no—
324C22×D3—202no—
325C22×D3—202no—
326C3×Q8—102no—
327C3×Q8—102no—
328C3×Q8—202no—
329C2×C3×C4—22no—
330C2×C3×C4—42no—
331C2×C3×C4—102no—
332C2×C3×C4—202no—
333C2×C3×C4C2×D2012yes—
334C2×C3×C4D4×D511yescharacteristic
335C2×C3×C4#71312yes—
336C2×C3×C4C23×D511yescharacteristic
337C2×Dic3—22no—
338C2×Dic3—42no—
339C2×Dic3—52no—
340C2×Dic3—102no—
341D12—102no—
342D12—102no—
343D12—208no—
344D12—202no—
345C4×D3—102no—
346C4×D3—102no—
347C4×D3—104no—
348C3×C8—102no—
349C3⋊C8C2×D2014yescomplemented
350C22×C5#88412yes—
351C22×C5#91412yes—
352C22×C5#91812yes—
353C22×C5C2×D3×D411yescharacteristic
354C2×D5—62no—
355C2×D5—62no—
356C2×D5—62no—
357C2×D5—124no—
358C2×D5—122no—
359C2×D5—122no—
360C2×D5—122no—
361C2×D5—244no—
362C4×C5—42no—
363C4×C5—122no—
364C4×C5#88412yes—
365C4×C5C2×#23511yescharacteristic
366C4×C5C2×D3×D411yescharacteristic
367Dic5—42no—
368Dic5—62no—
369C24—151no—
370C24—301no—
371C2×Q8—52no—
372C2×Q8—101no—
373C2×Q8—102no—
374C2×Q8—102no—
375C2×D4—152no—
376C2×D4—304no—
377C2×D4—302no—
378C2×D4—302no—
379C2×D4—301no—
380C2×D4—604no—
381C22×C4—21no—
382C22×C4—61no—
383C22×C4—101no—
384C22×C4—151no—
385C22×C4—152no—
386C22×C4—152no—
387C22×C4—302no—
388C22×C4—302no—
389C22×C4C2×D3×D511yescharacteristic
390SD16—308no—
391M16—308no—
392C2×C8—34no—
393C2×C8—32no—
394C2×C8—52no—
395C2×C8—102no—
396C4⋊C4—21no—
397C4⋊C4—32no—
398C4⋊C4—61no—
399C4⋊C4—304no—
400C4⋊C4C2×D3×D512yes—
401C22⋊C4—304no—
402C22⋊C4—304no—
403C3×C5C2×#46811yescharacteristic, complemented, Hall
404C22×C3#404112yes—
405C22×C3#405712yes—
406C22×C3#406412yes—
407C22×C3C2×D4×D511yescharacteristic
408C2×D3—102no—
409C2×D3—102no—
410C2×D3—102no—
411C2×D3—204no—
412C2×D3—202no—
413C2×D3—202no—
414C2×D3—202no—
415C2×D3—404no—
416C3×C4—42no—
417C3×C4—202no—
418C3×C4#404112yes—
419C3×C4C22×D2011yescharacteristic
420C3×C4C2×#71311yescharacteristic
421Dic3—42no—
422Dic3—102no—
423C2×C5#481214yescomplemented
424C2×C5C2×#88411yescharacteristic
425C2×C5C2×#91411yescharacteristic
426C2×C5C2×#91811yescharacteristic
427D5—122no—
428D5—242no—
429C23—152no—
430C23—302no—
431C23—302no—
432C23—302no—
433C23—302no—
434C23—602no—
435C23—602no—
436C23—602no—
437C23#679011yescharacteristic
438Q8—102no—
439Q8—102no—
440Q8—202no—
441D4—302no—
442D4—302no—
443D4—608no—
444D4—602no—
445C2×C4—22no—
446C2×C4—42no—
447C2×C4—62no—
448C2×C4—102no—
449C2×C4—122no—
450C2×C4—152no—
451C2×C4—202no—
452C2×C4—302no—
453C2×C4—304no—
454C2×C4—302no—
455C2×C4—302no—
456C2×C4#677312yes—
457C2×C4D3×D2012yes—
458C2×C4#679011yescharacteristic
459C2×C4C22×D3×D511yescharacteristic
460C8—34no—
461C8—102no—
462C2×C3#6517514yescomplemented
463C2×C3C2×#404111yescharacteristic
464C2×C3C2×#405711yescharacteristic
465C2×C3C2×#406411yescharacteristic
466D3—202no—
467D3—402no—
468C5C2×#481211yescharacteristic, complemented, Sylow
469C22—302no—
470C22—302no—
471C22—302no—
472C22—604no—
473C22—602no—
474C22—602no—
475C22—602no—
476C22—1204no—
477C22#9145912yes—
478C22#9150012yes—
479C22#9151212yes—
480C22C2×#679011yescharacteristic
481C4—42no—
482C4—122no—
483C4—202no—
484C4—302no—
485C4#9145912yes—
486C4C2×#677311yescharacteristic
487C4C2×D3×D2011yescharacteristic
488C3C2×#6517511yescharacteristic, complemented, Sylow
489C2—602no—
490C2—1202no—
491C2#1174735614yesdirect product factor
492C2C2×#9145911yescharacteristic
493C2C2×#9150011yescharacteristic
494C2C2×#9151211yescharacteristic
subgroupG/H
centerC23#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC2×#91784C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#468
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#91390C2semidirect
3. C22×#6658C2semidirect
4. C22×#6651C2semidirect
5. C2×C5×#807C2semidirect
6. C2×C3×#3942C2semidirect
7. C2×#90969C2semidirect
8. #11747356C2direct (N × H)
24. #91390C22semidirect
26. C2×#6658C22semidirect
28. C2×#6651C22semidirect
29. C5×#807C22semidirect
30. C3×#3942C22semidirect
31. #90969C22semidirect
38. C2×#3942D3semidirect
67. C2×C5×C3⋊C8D4semidirect
81. C2×#807D5semidirect
103. #3942C2×D3semidirect
138. C5×C3⋊C8C2×D4semidirect
160. #807C2×D5semidirect
253. C2×C3⋊C8D20semidirect
311. C2×C3×C5#468semidirect
349. C3⋊C8C2×D20semidirect
403. C3×C5C2×#468semidirect
423. C2×C5#4812semidirect
462. C2×C3#65175semidirect
468. C5C2×#4812semidirect
488. C3C2×#65175semidirect
491. C2#11747356direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#917842
C2×#913902
C22×#66582
C22×#66512
C2×C5×#8072
C2×C3×#39422
C2×#909692
#117473562
C2×#651753
C2×#48125